Recently Solecki (1996) has shown that a differential equation for vib
ration of a rectangular plate with a cutout can be reduced to boundary
integral equations. This was accomplished by filling the cutout with
a ''patch'' made of the same material as the rest of the plate and sep
arated from it by an infinitesimal gap. Thanks to this procedure it wa
s possible to apply finite Fourier transformation of discontinuous fun
ctions in a rectangular domain. Subsequent application of the availabl
e boundary conditions led to a system of boundary integral equations.
A plate simply supported along the perimeter, and fixed along the cuto
ut (an L-shaped plate), was analyzed as an example. The general soluti
on obtained by Solecki (1996) serves here to determine the frequencies
of natural vibration of a L-shaped plate simply supported all around
its perimeter. This problem is, however, more complicated than the pre
vious example: to satisfy the boundary conditions an infinite series d
epending on discontinuous functions must be differentiated The theoret
ical development is illustrated by numerical values of the frequencies
of the natural vibrations of a square plate with a square cutout. The
results are compared with the results obtained using finite elements
method.